Question

Solve $\int \left(\frac{x^2+5x+2}{x+2}\right)dx$.

Answer 1

$\int \frac{x^2+5x+2}{x+2}dx$

$=\int \left[\frac{(x+2)(x+3)-4}{(x+2)}\right]dx$

$=\int \left[\right(x+3)-\frac{4}{x+2}]dx$

$=\int xdx+\int 3dx-4\int \frac{dx}{x+2}$

$=\frac{x^2}{2}+3x-4log|x+2|+C$

$\because \int \left(\frac{x^2+5x+2}{x+2}\right)dx=\frac{x^2}{2}+3x-4log|x+2|+C$